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<h1 class="title">Pre-analysis plan for ‘Does good news about climate change motivate action?’</h1>
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<section id="motivation-and-background" class="level2">
<h2 class="anchored" data-anchor-id="motivation-and-background">Motivation and background</h2>
<p>We want to understand how informing Americans about recent successes in fighting climate change affects their attitudes about climate change, including both how worried they are about the problem and how willing they are to support costly action to do something about it.</p>
<p>Even as public awareness and concern about climate change has increased, there have been encouraging pieces of good news in recent years: renewable energy has gotten dramatically cheaper to produce, employment in renewable energy has grown substantially, US emissions have dropped along with those of many other countries, and the US government is devoting considerably more resources to the problem. We speculate (and can confirm based on our pre-test) that many of these facts are not widely known; we will document the extent of this knowledge in our survey.</p>
<p>Our main focus is on the effects of informing Americans about the recent “good news” in climate change. Does informing Americans about these facts make them less worried? Does it make them less willing to take costly action (because it seems that the problem is less serious than they thought) or more willing to take costly action (because it seems that their effort is more likely to pay off, and/or because the problem is more likely to be solved than they thought)?</p>
<p>We will investigate these problems using a survey experiment with US respondents recruited via Prolific.</p>
</section>
<section id="data-recoding" class="level2">
<h2 class="anchored" data-anchor-id="data-recoding">Data recoding</h2>
<p>We conducted a pilot of our survey with 100 respondents on May 2, 2023. We will use a slightly updated version of that survey in our full data collection. In this document we will use the data from this pre-test (with slight updates to reflect changes we have made to the survey) to show what analysis we will conduct with the final data.</p>
<div class="cell">
<div class="cell-output cell-output-stderr">
<pre><code>── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──</code></pre>
</div>
<div class="cell-output cell-output-stderr">
<pre><code>✔ ggplot2 3.4.0      ✔ purrr   1.0.1 
✔ tibble  3.1.8      ✔ dplyr   1.0.10
✔ tidyr   1.3.0      ✔ stringr 1.5.0 
✔ readr   2.1.1      ✔ forcats 0.5.1 </code></pre>
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<div class="cell-output cell-output-stderr">
<pre><code>── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()</code></pre>
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</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co"># A function for loading in the data to deal with column names etc </span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>qualtrics_load <span class="ot">&lt;-</span> <span class="cf">function</span>(file_path){</span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>  the_colnames <span class="ot">&lt;-</span> <span class="fu">read_csv</span>(file_path) <span class="sc">|&gt;</span> <span class="fu">colnames</span>()</span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">read_csv</span>(file_path, <span class="at">skip =</span> <span class="dv">3</span>, <span class="at">col_names =</span> F) <span class="sc">|&gt;</span> </span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a>    <span class="fu">setNames</span>(the_colnames) <span class="sc">|&gt;</span></span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a>    <span class="fu">filter</span>(consent <span class="sc">==</span> <span class="st">"Yes, I understand and consent to take part in the survey"</span>) <span class="sc">|&gt;</span> </span>
<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a>    <span class="fu">select</span>(<span class="sc">-</span>StartDate, <span class="sc">-</span>EndDate, <span class="sc">-</span>Status, <span class="sc">-</span>Progress, <span class="sc">-</span>RecordedDate, <span class="sc">-</span>ResponseId, <span class="sc">-</span>DistributionChannel, <span class="sc">-</span>UserLanguage, <span class="sc">-</span>prolific_id, <span class="sc">-</span>consent)</span>
<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a>pt <span class="ot">&lt;-</span> <span class="fu">qualtrics_load</span>(<span class="st">"./../SSI3 final survey 2023 (SSD)_May 5, 2023_07.46.csv"</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stderr">
<pre><code>Rows: 102 Columns: 66
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (66): StartDate, EndDate, Status, Progress, Duration (in seconds), Finis...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
Rows: 100 Columns: 66
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr  (54): X3, X8, X9, X10, X11, X12, X14, X15, X16, X17, X18, X20, X21, X22...
dbl   (5): X4, X5, X13, X31, X46
lgl   (4): X6, X19, X39, X41
dttm  (3): X1, X2, X7

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.</code></pre>
</div>
</div>
<p>Here we add the new columns and fix a typo in one of the response choices:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>pt <span class="sc">|&gt;</span> </span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">hh_income =</span> <span class="fu">sample</span>(<span class="at">x =</span> <span class="fu">c</span>(<span class="st">"Less than $25,000"</span>, <span class="st">"$25,000-$49,999"</span>, <span class="st">"$50,000-$74,999"</span>, <span class="st">"$75,000-$99,000"</span>, <span class="st">"$100,000-$149,999"</span>, <span class="st">"$150,000 or more"</span>, <span class="st">"Prefer not to say"</span>), <span class="at">size =</span> <span class="fu">n</span>(), <span class="at">replace =</span> T, <span class="at">prob =</span> <span class="fu">c</span>(.<span class="dv">1</span>, .<span class="dv">2</span>, .<span class="dv">3</span>, .<span class="dv">15</span>, .<span class="dv">1</span>, .<span class="dv">05</span>, .<span class="dv">1</span>)),</span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a>         <span class="at">attention_check =</span> <span class="fu">sample</span>(<span class="at">x =</span> <span class="fu">c</span>(<span class="st">"Strongly disagree,Neither agree nor disagree"</span>, <span class="st">"Strongly disagree"</span>, <span class="st">"Strongly agree"</span>, <span class="st">"Somewhat agree"</span>), <span class="at">size =</span> <span class="fu">n</span>(), <span class="at">replace =</span> T, <span class="at">prob =</span> <span class="fu">c</span>(.<span class="dv">9</span>, .<span class="dv">05</span>, .<span class="dv">03</span>, .<span class="dv">02</span>)),</span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a>        <span class="at">emissions_prediction =</span> <span class="fu">sample</span>(<span class="at">x =</span> <span class="fu">c</span>(<span class="st">"Definitely not"</span>, <span class="st">"Probably not"</span>, <span class="st">"Possibly"</span>, <span class="st">"Probably"</span>, <span class="st">"Very probably"</span>, <span class="st">"Definitely"</span>), <span class="at">size =</span> <span class="fu">n</span>(), <span class="at">replace =</span> T, <span class="at">prob =</span> <span class="fu">c</span>(.<span class="dv">35</span>, .<span class="dv">25</span>, .<span class="dv">15</span>, .<span class="dv">15</span>, .<span class="dv">08</span>, .<span class="dv">02</span>))) <span class="sc">|&gt;</span> </span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="co">#          emissions_prediction = sample(x = c(str_c("increased by ", c("75%", "50%", "25%")), "about the same", str_c("reduced by ", c("75%", "50%", "25%"))), size = n(), replace = T, prob = c(.05, .1, .15, .2, .05, .15, .3 ))) |&gt; </span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">concern_cc_pre =</span> <span class="fu">ifelse</span>(concern_cc_pre <span class="sc">==</span> <span class="st">"Not concerned at al"</span>, <span class="st">"Not concerned at all"</span>, concern_cc_pre)) <span class="ot">-&gt;</span> pt_full</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>The data we receive after data collection should look like that.</p>
<p>Now we do some recoding and combining:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>great_deal_levels <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">"Not at all"</span>, <span class="st">"A little"</span>, <span class="st">"Somewhat"</span>, <span class="st">"A lot"</span>, <span class="st">"A great deal"</span>)</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>agreement_levels <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">"Strongly disagree"</span>, <span class="st">"Somewhat disagree"</span>, <span class="st">"Neither agree nor disagree"</span>, <span class="st">"Somewhat agree"</span>, <span class="st">"Strongly agree"</span>)</span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>pt_full <span class="sc">|&gt;</span> </span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">id =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">n</span>(), <span class="co"># for merging in knowledge scores later</span></span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>         </span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a>         <span class="do">### demographics</span></span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a>         <span class="at">education =</span> <span class="fu">factor</span>(education, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"Some high school"</span>, <span class="st">"High school graduate"</span>, <span class="st">"Some college"</span>, <span class="st">"2-year college degree"</span>, <span class="st">"4-year college degree"</span>, <span class="st">"Postgraduate degree (MA, MBA, MD, JD, PhD, etc.)"</span>), <span class="at">ordered =</span> T),</span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a>         <span class="at">lib_con =</span> <span class="fu">factor</span>(lib_con, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"Very conservative"</span>, <span class="st">"Conservative"</span>, <span class="st">"Moderate"</span>, <span class="st">"Liberal"</span>, <span class="st">"Very liberal"</span>), <span class="at">ordered =</span> T),</span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a>         <span class="at">hh_income =</span> <span class="fu">factor</span>(hh_income, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"Less than $25,000"</span>, <span class="st">"$25,000-$49,999"</span>, <span class="st">"$50,000-$74,999"</span>, <span class="st">"Prefer not to say"</span>, <span class="st">"$75,000-$99,000"</span>, <span class="st">"$100,000-$149,999"</span>, <span class="st">"$150,000 or more"</span>), <span class="at">ordered =</span> T),</span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a>         <span class="at">hh_income_missing =</span> <span class="fu">as.integer</span>(hh_income <span class="sc">==</span> <span class="st">"Prefer not to say"</span>),</span>
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a>         </span>
<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a>         <span class="do">### pre-treatment attitudes</span></span>
<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a>         <span class="at">concern_cc_pre =</span> <span class="fu">factor</span>(concern_cc_pre, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"Not concerned at all"</span>, <span class="st">"Slightly concerned"</span>, <span class="st">"Moderately concerned"</span>, <span class="st">"Very concerned"</span>, <span class="st">"Extremely concerned"</span>), <span class="at">ordered =</span> T),</span>
<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a>         <span class="at">efficacy_pre =</span> <span class="fu">factor</span>(efficacy_pre, <span class="at">levels =</span> agreement_levels, <span class="at">ordered =</span> T),</span>
<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a>         </span>
<span id="cb7-16"><a href="#cb7-16" aria-hidden="true" tabindex="-1"></a>         <span class="do">### self-assessed knowledge beforehand </span></span>
<span id="cb7-17"><a href="#cb7-17" aria-hidden="true" tabindex="-1"></a>         <span class="at">know_cc_pre =</span> <span class="fu">recode</span>(know_cc_pre, <span class="sc">!!!</span><span class="fu">list</span>(<span class="st">"Not knowledgeable at all"</span> <span class="ot">=</span> <span class="st">"Not at all"</span>, <span class="st">"Slightly knowledgeable"</span> <span class="ot">=</span> <span class="st">"Slightly"</span>, <span class="st">"Moderately knowledgeable"</span> <span class="ot">=</span> <span class="st">"Moderately"</span>, <span class="st">"Very knowledgeable"</span> <span class="ot">=</span> <span class="st">"Very"</span>, <span class="st">"Extremely knowledgeable"</span> <span class="ot">=</span> <span class="st">"Extremely"</span>)),</span>
<span id="cb7-18"><a href="#cb7-18" aria-hidden="true" tabindex="-1"></a>         <span class="at">know_cc_pre =</span> <span class="fu">factor</span>(know_cc_pre, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"Not at all"</span>, <span class="st">"Slightly"</span>, <span class="st">"Moderately"</span>, <span class="st">"Very"</span>, <span class="st">"Extremely"</span>), <span class="at">ordered =</span> T),</span>
<span id="cb7-19"><a href="#cb7-19" aria-hidden="true" tabindex="-1"></a>        </span>
<span id="cb7-20"><a href="#cb7-20" aria-hidden="true" tabindex="-1"></a>         <span class="co"># how many of the good news prompts did they get?</span></span>
<span id="cb7-21"><a href="#cb7-21" aria-hidden="true" tabindex="-1"></a>         <span class="co"># these are the information treatments</span></span>
<span id="cb7-22"><a href="#cb7-22" aria-hidden="true" tabindex="-1"></a>         <span class="at">n_good_news_wo_ira =</span> <span class="fu">as.integer</span>(jobs_info <span class="sc">==</span> <span class="st">"included"</span>) <span class="sc">+</span> <span class="fu">as.integer</span>(us_emissions_info <span class="sc">==</span> <span class="st">"included"</span>) <span class="sc">+</span> <span class="fu">as.integer</span>(solar_cost_info <span class="sc">==</span> <span class="st">"included"</span>), </span>
<span id="cb7-23"><a href="#cb7-23" aria-hidden="true" tabindex="-1"></a>         <span class="co"># and this includes the IRA description as a piece of good news (which could affect concern etc)</span></span>
<span id="cb7-24"><a href="#cb7-24" aria-hidden="true" tabindex="-1"></a>         <span class="at">n_good_news_w_ira =</span> n_good_news_wo_ira <span class="sc">+</span> <span class="fu">as.integer</span>(FL_39_DO <span class="sc">==</span> <span class="st">"FL_41|Concern,taxes,andefficacy"</span>),</span>
<span id="cb7-25"><a href="#cb7-25" aria-hidden="true" tabindex="-1"></a>         </span>
<span id="cb7-26"><a href="#cb7-26" aria-hidden="true" tabindex="-1"></a>         <span class="do">### post-treatment outcomes</span></span>
<span id="cb7-27"><a href="#cb7-27" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-28"><a href="#cb7-28" aria-hidden="true" tabindex="-1"></a>         <span class="do">## general attitudes/beliefs</span></span>
<span id="cb7-29"><a href="#cb7-29" aria-hidden="true" tabindex="-1"></a>         <span class="co"># concern about climate change</span></span>
<span id="cb7-30"><a href="#cb7-30" aria-hidden="true" tabindex="-1"></a>         <span class="at">how_worried =</span> <span class="fu">factor</span>(how_worried, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"Not at all worried"</span>, <span class="st">"A little worried"</span>, <span class="st">"Moderately worried"</span>, <span class="st">"Very worried"</span>, <span class="st">"Extremely worried"</span>), <span class="at">ordered =</span> T),</span>
<span id="cb7-31"><a href="#cb7-31" aria-hidden="true" tabindex="-1"></a>         <span class="at">how_affect_you =</span> <span class="fu">factor</span>(how_affect_you, <span class="at">levels =</span> great_deal_levels, <span class="at">ordered =</span> T),</span>
<span id="cb7-32"><a href="#cb7-32" aria-hidden="true" tabindex="-1"></a>         <span class="at">how_affect_US =</span> <span class="fu">factor</span>(how_affect_US, <span class="at">levels =</span> great_deal_levels, <span class="at">ordered =</span> T),</span>
<span id="cb7-33"><a href="#cb7-33" aria-hidden="true" tabindex="-1"></a>         <span class="at">how_affect_future =</span> <span class="fu">factor</span>(how_affect_future, <span class="at">levels =</span> great_deal_levels, <span class="at">ordered =</span> T),</span>
<span id="cb7-34"><a href="#cb7-34" aria-hidden="true" tabindex="-1"></a>         <span class="at">concern_index =</span> (<span class="fu">as.integer</span>(how_worried) <span class="sc">+</span> <span class="fu">as.integer</span>(how_affect_you) <span class="sc">+</span> <span class="fu">as.integer</span>(how_affect_US) <span class="sc">+</span> <span class="fu">as.integer</span>(how_affect_US) <span class="sc">-</span> <span class="dv">4</span>)<span class="sc">/</span><span class="dv">16</span>, <span class="co"># so it's zero to 1</span></span>
<span id="cb7-35"><a href="#cb7-35" aria-hidden="true" tabindex="-1"></a>         </span>
<span id="cb7-36"><a href="#cb7-36" aria-hidden="true" tabindex="-1"></a>         <span class="co"># efficacy measures</span></span>
<span id="cb7-37"><a href="#cb7-37" aria-hidden="true" tabindex="-1"></a>         <span class="at">believe_can_do_sthg =</span> <span class="fu">factor</span>(believe_can_do_sthg, <span class="at">levels =</span> agreement_levels, <span class="at">ordered =</span> T),</span>
<span id="cb7-38"><a href="#cb7-38" aria-hidden="true" tabindex="-1"></a>         <span class="at">collective_efficacy =</span> <span class="fu">factor</span>(collective_efficacy, <span class="at">levels =</span> agreement_levels, <span class="at">ordered =</span> T),</span>
<span id="cb7-39"><a href="#cb7-39" aria-hidden="true" tabindex="-1"></a>         <span class="at">combined_efficacy_post =</span> (<span class="fu">as.integer</span>(believe_can_do_sthg) <span class="sc">+</span> <span class="fu">as.integer</span>(collective_efficacy) <span class="sc">-</span> <span class="dv">2</span>)<span class="sc">/</span><span class="dv">8</span>,</span>
<span id="cb7-40"><a href="#cb7-40" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-41"><a href="#cb7-41" aria-hidden="true" tabindex="-1"></a>         <span class="co"># optimism</span></span>
<span id="cb7-42"><a href="#cb7-42" aria-hidden="true" tabindex="-1"></a>         <span class="at">emissions_prediction =</span> <span class="fu">factor</span>(emissions_prediction, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"Definitely not"</span>, <span class="st">"Probably not"</span>, <span class="st">"Possibly"</span>, <span class="st">"Probably"</span>, <span class="st">"Very probably"</span>, <span class="st">"Definitely"</span>), <span class="at">ordered =</span> T),</span>
<span id="cb7-43"><a href="#cb7-43" aria-hidden="true" tabindex="-1"></a>         </span>
<span id="cb7-44"><a href="#cb7-44" aria-hidden="true" tabindex="-1"></a>         <span class="co"># policy attitudes</span></span>
<span id="cb7-45"><a href="#cb7-45" aria-hidden="true" tabindex="-1"></a>         <span class="co"># attitude toward IRA</span></span>
<span id="cb7-46"><a href="#cb7-46" aria-hidden="true" tabindex="-1"></a>         <span class="at">ira_response =</span> <span class="fu">ifelse</span>(<span class="fu">is.na</span>(ira_treatment_q), ira_control_q, ira_treatment_q),</span>
<span id="cb7-47"><a href="#cb7-47" aria-hidden="true" tabindex="-1"></a>         <span class="at">ira_response =</span> <span class="fu">factor</span>(ira_response, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"Goes much too far"</span>, <span class="st">"Goes somewhat too far"</span>, <span class="st">"Is about right"</span>, <span class="st">"Should go somewhat further"</span>, <span class="st">"Should go much further"</span>), <span class="at">ordered =</span> T),</span>
<span id="cb7-48"><a href="#cb7-48" aria-hidden="true" tabindex="-1"></a>         </span>
<span id="cb7-49"><a href="#cb7-49" aria-hidden="true" tabindex="-1"></a>         <span class="co"># willingness to pay taxes</span></span>
<span id="cb7-50"><a href="#cb7-50" aria-hidden="true" tabindex="-1"></a>         <span class="at">wtp_taxes =</span> <span class="fu">factor</span>(wtp_taxes, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"Totally unwilling"</span>, <span class="st">"A little willing"</span>, <span class="st">"Moderately willing"</span>, <span class="st">"Very willing"</span>, <span class="st">"Extremely willing"</span>), <span class="at">ordered =</span> T)) <span class="sc">|&gt;</span></span>
<span id="cb7-51"><a href="#cb7-51" aria-hidden="true" tabindex="-1"></a>  </span>
<span id="cb7-52"><a href="#cb7-52" aria-hidden="true" tabindex="-1"></a>  <span class="co"># code correct knowledge questions</span></span>
<span id="cb7-53"><a href="#cb7-53" aria-hidden="true" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">correct_1_CO2 =</span> <span class="fu">as.integer</span>(know_co2_meaning <span class="sc">==</span> <span class="st">"Carbon dioxide"</span>),</span>
<span id="cb7-54"><a href="#cb7-54" aria-hidden="true" tabindex="-1"></a>         <span class="at">correct_2_GreenhouseEffect =</span> <span class="fu">as.integer</span>(know_main_cause_gw <span class="sc">==</span> <span class="st">"Increased emissions of greenhouse gasses (the so-called greenhouse effect)"</span>),</span>
<span id="cb7-55"><a href="#cb7-55" aria-hidden="true" tabindex="-1"></a>         <span class="at">correct_3_EarthquakesNotCC =</span> <span class="fu">as.integer</span>(know_not_gw <span class="sc">==</span> <span class="st">"Earthquakes"</span>),</span>
<span id="cb7-56"><a href="#cb7-56" aria-hidden="true" tabindex="-1"></a>         <span class="at">correct_4_WhatWouldHelp =</span> <span class="fu">as.integer</span>(know_what_helps <span class="sc">==</span> <span class="st">"All of the above"</span>),</span>
<span id="cb7-57"><a href="#cb7-57" aria-hidden="true" tabindex="-1"></a>         <span class="at">correct_5_WindIsRenewable =</span> <span class="fu">as.integer</span>(know_renewable <span class="sc">==</span> <span class="st">"Wind"</span>),</span>
<span id="cb7-58"><a href="#cb7-58" aria-hidden="true" tabindex="-1"></a>         <span class="at">correct_6_BidenPolicy =</span> <span class="fu">as.integer</span>(know_ira_dcr <span class="sc">==</span> <span class="st">"Tax credits for people who purchase electric vehicles made in the US"</span>),</span>
<span id="cb7-59"><a href="#cb7-59" aria-hidden="true" tabindex="-1"></a>         <span class="at">correct_7_USGasTaxLow =</span> <span class="fu">as.integer</span>(know_gas_tax <span class="sc">==</span> <span class="dv">0</span>),</span>
<span id="cb7-60"><a href="#cb7-60" aria-hidden="true" tabindex="-1"></a>         <span class="at">correct_8_SolarWindJobs =</span> <span class="fu">as.integer</span>(know_jobs <span class="sc">==</span> <span class="st">"Around 480,000, or four times as many"</span>),</span>
<span id="cb7-61"><a href="#cb7-61" aria-hidden="true" tabindex="-1"></a>         <span class="at">correct_9_USCO2Drop =</span> <span class="fu">as.integer</span>(know_co2_change <span class="sc">==</span> <span class="st">"It went down by about 15%, to 5 billion tons"</span>),</span>
<span id="cb7-62"><a href="#cb7-62" aria-hidden="true" tabindex="-1"></a>         <span class="at">correct_10_SolarCostDrop =</span> <span class="fu">as.integer</span>(know_solar_cost <span class="sc">==</span> <span class="st">"The cost has gone down by around 80%"</span>)) <span class="sc">|&gt;</span> </span>
<span id="cb7-63"><a href="#cb7-63" aria-hidden="true" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">know_jobs =</span> <span class="fu">factor</span>(know_jobs, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"Around 30,000, or one-fourth as many"</span>, <span class="st">"Around 60,000, or half as many"</span>, <span class="st">"Around 120,000, or the same number"</span>, <span class="st">"Around 240,000, or twice as many"</span>, <span class="st">"Around 480,000, or four times as many"</span>), <span class="at">ordered =</span> T),</span>
<span id="cb7-64"><a href="#cb7-64" aria-hidden="true" tabindex="-1"></a>         <span class="at">know_co2_change =</span> <span class="fu">factor</span>(know_co2_change, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"It went down by about 30%, to 4 billion tons"</span>, <span class="st">"It went down by about 15%, to 5 billion tons"</span>, <span class="st">"It stayed about the same (6 billion tons)"</span>, <span class="st">"It went up by about 15%, to 7 billion tons"</span>, <span class="st">"It went up by about 30%, to 8 billion tons"</span>), <span class="at">ordered =</span> T),</span>
<span id="cb7-65"><a href="#cb7-65" aria-hidden="true" tabindex="-1"></a>         <span class="at">know_solar_cost =</span> <span class="fu">factor</span>(know_solar_cost, <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"The cost has gone down by around 80%"</span>, <span class="st">"The cost has gone down by about 40%"</span>, <span class="st">"The cost has stayed about the same"</span>, <span class="st">"The cost has gone up by about 40%"</span>, <span class="st">"The cost has gone up by about 80%"</span>), <span class="at">ordered =</span> T)) <span class="ot">-&gt;</span> pt_full_recoded</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Knowledge scores (for exploratory analysis):</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="co"># get pct correct </span></span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>pt_full_recoded <span class="sc">|&gt;</span> </span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">select</span>(id, <span class="fu">starts_with</span>(<span class="st">"correct_"</span>)) <span class="sc">|&gt;</span> </span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">pivot_longer</span>(<span class="at">cols =</span> <span class="sc">-</span>id, <span class="at">names_prefix =</span> <span class="st">"correct_"</span>, <span class="at">names_to =</span> <span class="st">"question"</span>, <span class="at">values_to =</span> <span class="st">"correct"</span>) <span class="sc">|&gt;</span> </span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">group_by</span>(id) <span class="sc">|&gt;</span> </span>
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a>  <span class="fu">summarize</span>(<span class="at">pct_correct =</span> <span class="fu">mean</span>(correct, <span class="at">na.rm =</span> T)) <span class="ot">-&gt;</span> correct_pcts</span>
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a>pt_full_recoded <span class="sc">|&gt;</span> </span>
<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a>  <span class="fu">select</span>(id, <span class="fu">starts_with</span>(<span class="st">"correct_"</span>)) <span class="sc">|&gt;</span> </span>
<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a>  <span class="fu">pivot_longer</span>(<span class="at">cols =</span> <span class="sc">-</span>id, <span class="at">names_prefix =</span> <span class="st">"correct_"</span>, <span class="at">names_to =</span> <span class="st">"question"</span>, <span class="at">values_to =</span> <span class="st">"correct"</span>) <span class="sc">|&gt;</span> </span>
<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a>  <span class="fu">filter</span>(<span class="fu">str_detect</span>(question, <span class="st">"^8"</span>) <span class="sc">|</span> <span class="fu">str_detect</span>(question, <span class="st">"^9"</span>) <span class="sc">|</span> <span class="fu">str_detect</span>(question, <span class="st">"^10"</span>)) <span class="sc">|&gt;</span> </span>
<span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a>  <span class="fu">group_by</span>(id) <span class="sc">|&gt;</span> </span>
<span id="cb8-13"><a href="#cb8-13" aria-hidden="true" tabindex="-1"></a>  <span class="fu">summarize</span>(<span class="at">pct_correct_good_news =</span> <span class="fu">mean</span>(correct, <span class="at">na.rm =</span> T)) <span class="ot">-&gt;</span> correct_pcts_gn</span>
<span id="cb8-14"><a href="#cb8-14" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-15"><a href="#cb8-15" aria-hidden="true" tabindex="-1"></a>pt_full_recoded <span class="sc">|&gt;</span> </span>
<span id="cb8-16"><a href="#cb8-16" aria-hidden="true" tabindex="-1"></a>  <span class="fu">left_join</span>(correct_pcts, <span class="at">by =</span> <span class="st">"id"</span>) <span class="sc">|&gt;</span> </span>
<span id="cb8-17"><a href="#cb8-17" aria-hidden="true" tabindex="-1"></a>  <span class="fu">left_join</span>(correct_pcts_gn, <span class="at">by =</span> <span class="st">"id"</span>) <span class="ot">-&gt;</span> dat </span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="sketch-of-theory-as-motivation-for-analysis-approach" class="level2">
<h2 class="anchored" data-anchor-id="sketch-of-theory-as-motivation-for-analysis-approach">Sketch of theory as motivation for analysis approach</h2>
<p>We want to know whether (and to what extent) providing “good news” about climate change affects respondents’ policy preferences.</p>
<p>We expect that the three pieces of good news we have selected will move respondents’ beliefs as follows:</p>
<ul>
<li>the US emissions message will make (some of) them think that reducing US emissions is easier and further along than they thought</li>
<li>the solar cost message will make (some of) them think that decarbonization is cheaper and more technically achievable than they thought</li>
<li>the renewable jobs message will make (some of) them think that decarbonization is more achievable and more beneficial to American workers than they thought</li>
</ul>
<p>Individually, these messages are conveying different information and may lead respondents to arrive at different conclusions about climate change policy. Broadly, though, we expect that providing more of this information will lead respondents to perceive climate change as a more manageable problem. We hypothesize that respondents who receive more of this information will feel less concerned about climate change, more confident that individual and/or collective action toward climate change is effective, and will be more optimistic about reducing emissions globally (<strong>Hypothesis Family A</strong>). We also hypothesize that respondents who receive more of this information will be more enthusiastic about supporting the fight against climate change, as measured by willingness to pay taxes to support a more aggressive US policy, support for the IRA and further policy in that direction, and willingness to donate to an NGO who supported the IRA and works on climate change policy (<strong>Hypothesis Family B</strong>).</p>
</section>
<section id="hypothesis-family-a-concern-optimism-and-efficacy" class="level2">
<h2 class="anchored" data-anchor-id="hypothesis-family-a-concern-optimism-and-efficacy">Hypothesis family A: Concern, optimism, and efficacy</h2>
<p>These hypotheses relate to attitudes and beliefs that we consider to be inputs to policy preferences. These are factors that someone might take into consideration in deciding how much effort they think society should devote to this issue or how much they would be willing to pay in taxes. (Although we do not think anyone makes an explicit utility calculation, these are factors someone might use to do so.)</p>
<p>Those factors include</p>
<ul>
<li>Beliefs about <strong>efficacy of action</strong> against climate change. Learning that progress has already been made against climate change, and that technology changes make new strategies possible and cost-effective, could make respondents feel that additional effort (by themselves and/or by governments and others) would pay off more than they previously thought.</li>
<li>Beliefs about the extent of <strong>efforts that others are undertaking or will undertake</strong>. Learning that others are already involved (i.e.&nbsp;others are more involved than they thought) could make respondents feel that taking part would be more rewarding, whether because it speaks to efficacy of action (see above) or because it speaks to the likelihood of ultimate success (and they want to be part of something successful) or because they want to conform to others’ actions and avoid being seen as a free rider. It could also make them want to take <strong>less</strong> action because others’ actions might be sufficient.</li>
</ul>
<section id="hypothesis-a1-providing-more-good-news-increases-a-sense-of-efficacy-about-climate-change" class="level3">
<h3 class="anchored" data-anchor-id="hypothesis-a1-providing-more-good-news-increases-a-sense-of-efficacy-about-climate-change">Hypothesis A1: Providing more good news increases a sense of efficacy about climate change</h3>
<p>We will regress an index of post-treatment perceived efficacy (which combines personal and collective efficacy) about climate change on the number of pieces of good news experimentally provided and the strongest pre-treatment predictors of perceived efficacy (our pre-treatment measure of efficacy and ideology). The null hypothesis is that there is no effect of good news on efficacy, which implies no linear relationship between the two measures.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>efficacy_reg <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(combined_efficacy_post <span class="sc">~</span> n_good_news_wo_ira <span class="sc">+</span> <span class="fu">as.integer</span>(efficacy_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con), <span class="at">data =</span> dat)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="hypothesis-a2-providing-more-good-news-affects-beliefs-about-future-emissions" class="level3">
<h3 class="anchored" data-anchor-id="hypothesis-a2-providing-more-good-news-affects-beliefs-about-future-emissions">Hypothesis A2: Providing more good news affects beliefs about future emissions</h3>
<p>We will regress a numerical measure of the respondent’s confidence that emissions will drop by at least 50% by 2050 (0 = definitely not, 6 = definitely) on the number of pieces of good news experimentally provided and what we expect to be the strongest predictors of expected emissions (our pre-treatment measure of concern and ideology). The null hypothesis is that there is no effect of good news on predicted emissions, which implies no linear relationship between the two measures. Out prediction is that the relationship will be positive.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>emissions_reg <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(<span class="fu">as.integer</span>(emissions_prediction) <span class="sc">~</span> n_good_news_wo_ira <span class="sc">+</span> <span class="fu">as.integer</span>(concern_cc_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con), <span class="at">data =</span> dat)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="hypothesis-a3-providing-more-good-news-reduces-concern-about-climate-change" class="level3">
<h3 class="anchored" data-anchor-id="hypothesis-a3-providing-more-good-news-reduces-concern-about-climate-change">Hypothesis A3: Providing more good news reduces concern about climate change</h3>
<p>We will regress an index of concern about climate change on the number of pieces of good news experimentally provided and the strongest predictors of concern (our pre-treatment measure of concern and ideology). The null hypothesis is that there is no effect of good news on climate concern, which implies no linear relationship between the two measures. Our hypothesis is that this relationship will be negative.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>concern_reg <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(concern_index <span class="sc">~</span> n_good_news_wo_ira <span class="sc">+</span> <span class="fu">as.integer</span>(concern_cc_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con), <span class="at">data =</span> dat)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="multiple-testing-and-reporting" class="level3">
<h3 class="anchored" data-anchor-id="multiple-testing-and-reporting">Multiple testing and reporting</h3>
<p>We will report the raw p-values for each of the 3 tests above. We will also report which null hypotheses would be rejected if we seek a FWER for these 3 hypotheses of .05. (We consider the above three tests to be a “family” in the sense that we will assess whether good news impacts on policy-relevant attitudes by looking at all three tests, and would report that there is such an effect if we rejected at least one of these nulls; we want to limit the probability of a false rejection in making that claim.) We will determine the criteria for rejection (i.e.&nbsp;the raw p-value below which we reject the null hypothesis) using the simulation method described here: https://egap.org/resource/10-things-to-know-about-multiple-comparisons/ That is, we will repeatedly reshuffle treatment assignments and conduct all three tests, computing the highest raw p-value threshold <span class="math inline">\(p*\)</span> such that at least one null hypothesis is rejected in no more than 5% of these simulations.</p>
<p>The regression table will look roughly like this (here using the pre-test data):</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>modelsummary<span class="sc">::</span><span class="fu">modelsummary</span>(<span class="at">models =</span> <span class="fu">list</span>(<span class="st">"Expected emissions"</span> <span class="ot">=</span> emissions_reg,</span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>                                         <span class="st">"Concern"</span> <span class="ot">=</span> concern_reg,</span>
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a>                                         <span class="st">"Efficacy"</span> <span class="ot">=</span> efficacy_reg),</span>
<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a>                           <span class="at">coef_map =</span> <span class="fu">c</span>(<span class="st">"(Intercept)"</span> <span class="ot">=</span> <span class="st">"Intercept"</span>,</span>
<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a>                                        <span class="st">"n_good_news_wo_ira"</span> <span class="ot">=</span> <span class="st">"Num. good news items provided"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">

<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:center;"> Expected emissions </th>
   <th style="text-align:center;"> Concern </th>
   <th style="text-align:center;"> Efficacy </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Intercept </td>
   <td style="text-align:center;"> 3.373 </td>
   <td style="text-align:center;"> −0.154 </td>
   <td style="text-align:center;"> −0.027 </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:center;"> (0.558) </td>
   <td style="text-align:center;"> (0.037) </td>
   <td style="text-align:center;"> (0.065) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Num. good news items provided </td>
   <td style="text-align:center;"> −0.239 </td>
   <td style="text-align:center;"> −0.005 </td>
   <td style="text-align:center;"> 0.013 </td>
  </tr>
  <tr>
   <td style="text-align:left;box-shadow: 0px 1px">  </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (0.160) </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (0.014) </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (0.012) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Num.Obs. </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 100 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> R2 </td>
   <td style="text-align:center;"> 0.040 </td>
   <td style="text-align:center;"> 0.820 </td>
   <td style="text-align:center;"> 0.739 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> R2 Adj. </td>
   <td style="text-align:center;"> 0.010 </td>
   <td style="text-align:center;"> 0.815 </td>
   <td style="text-align:center;"> 0.731 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> AIC </td>
   <td style="text-align:center;"> 373.9 </td>
   <td style="text-align:center;"> −130.8 </td>
   <td style="text-align:center;"> −114.3 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> BIC </td>
   <td style="text-align:center;"> 386.9 </td>
   <td style="text-align:center;"> −117.8 </td>
   <td style="text-align:center;"> −101.3 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> RMSE </td>
   <td style="text-align:center;"> 1.49 </td>
   <td style="text-align:center;"> 0.12 </td>
   <td style="text-align:center;"> 0.13 </td>
  </tr>
</tbody>
</table>

</div>
</div>
<p>The rejections using MHT criteria will be somehow indicated in the table, perhaps by including p-values and identifying cases where nulls are rejected under the adjusted p-value threshold.</p>
</section>
</section>
<section id="hypothesis-family-b-policy-preferences" class="level2">
<h2 class="anchored" data-anchor-id="hypothesis-family-b-policy-preferences">Hypothesis Family B: Policy preferences</h2>
<p>These hypotheses relate to policy preferences.</p>
<section id="hypothesis-b1-providing-more-good-news-increases-willingness-to-pay-higher-taxes-to-support-more-aggressive-response-to-climate-change" class="level3">
<h3 class="anchored" data-anchor-id="hypothesis-b1-providing-more-good-news-increases-willingness-to-pay-higher-taxes-to-support-more-aggressive-response-to-climate-change">Hypothesis B1: Providing more good news increases willingness to pay higher taxes to support more aggressive response to climate change</h3>
<p>We will regress a numerical measure of willingness to pay higher taxes (+2 = extremely willing, -2 = totally unwilling) on the number of pieces of good news experimentally provided and the strongest predictors of willingness to pay higher taxes (our pre-treatment measures of concern and ideology, plus household income). The null hypothesis is that there is no effect of good news on how much tax the respondent is willing to pay, which implies no linear relationship between the two measures.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>wtp_reg <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(<span class="fu">as.integer</span>(wtp_taxes) <span class="sc">~</span> n_good_news_wo_ira <span class="sc">+</span> <span class="fu">as.integer</span>(concern_cc_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con) <span class="sc">+</span> <span class="fu">as.integer</span>(hh_income) <span class="sc">+</span> hh_income_missing, <span class="at">data =</span> dat)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="hypothesis-b2-providing-more-good-news-increases-support-for-aggressive-us-action-on-climate" class="level3">
<h3 class="anchored" data-anchor-id="hypothesis-b2-providing-more-good-news-increases-support-for-aggressive-us-action-on-climate">Hypothesis B2: Providing more good news increases support for aggressive US action on climate</h3>
<p>We will regress a numerical response about the IRA (+2 = should go much further, -2 = has gone much too far) on the number of pieces of good news provided and the strongest predictors of efficacy (our pre-treatment measures of concern and ideology). The null hypothesis is that there is no effect of good news on support for aggressive US action on climate, which implies no linear relationship between the two measures.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>ira_reg <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(<span class="fu">as.integer</span>(ira_response) <span class="sc">~</span> n_good_news_wo_ira <span class="sc">+</span> <span class="fu">as.integer</span>(concern_cc_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con), <span class="at">data =</span> dat)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="hypothesis-b3-providing-more-good-news-increases-willingness-to-donate" class="level3">
<h3 class="anchored" data-anchor-id="hypothesis-b3-providing-more-good-news-increases-willingness-to-donate">Hypothesis B3: Providing more good news increases willingness to donate</h3>
<p>We will regress the amount the respondent planned to donate from a $100 lottery victory on the number of pieces of good news experimentally provided (not including the IRA, as this was provided to everyone by this point in the survey) and the strongest predictors of willingness to pay higher taxes (our pre-treatment measures of concern and ideology, plus household income). The null hypothesis is that there is no effect of good news on willingness to donate, which implies no linear relationship between the two measures.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb15"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a>donate_reg <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(donate_amount_4 <span class="sc">~</span> n_good_news_wo_ira <span class="sc">+</span> <span class="fu">as.integer</span>(concern_cc_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con) <span class="sc">+</span> <span class="fu">as.integer</span>(hh_income) <span class="sc">+</span> hh_income_missing, <span class="at">data =</span> dat)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="mht-and-reporting" class="level3">
<h3 class="anchored" data-anchor-id="mht-and-reporting">MHT and reporting</h3>
<p>We will use the same procedure mentioned above for MHT.</p>
<p>Here is some reporting:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>modelsummary<span class="sc">::</span><span class="fu">modelsummary</span>(<span class="at">models =</span> <span class="fu">list</span>(<span class="st">"Willingness to pay higher taxes"</span> <span class="ot">=</span> wtp_reg,</span>
<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a>                                         <span class="st">"Support for more aggressive policy"</span> <span class="ot">=</span> ira_reg,</span>
<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a>                                         <span class="st">"Donation"</span> <span class="ot">=</span> donate_reg),</span>
<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a>                           <span class="at">coef_map =</span> <span class="fu">c</span>(<span class="st">"(Intercept)"</span> <span class="ot">=</span> <span class="st">"Intercept"</span>,</span>
<span id="cb16-5"><a href="#cb16-5" aria-hidden="true" tabindex="-1"></a>                                        <span class="st">"n_good_news_wo_ira"</span> <span class="ot">=</span> <span class="st">"Num. good news items provided"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">

<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:center;"> Willingness to pay higher taxes </th>
   <th style="text-align:center;"> Support for more aggressive policy </th>
   <th style="text-align:center;"> Donation </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Intercept </td>
   <td style="text-align:center;"> −0.059 </td>
   <td style="text-align:center;"> 0.909 </td>
   <td style="text-align:center;"> −8.910 </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:center;"> (0.329) </td>
   <td style="text-align:center;"> (0.337) </td>
   <td style="text-align:center;"> (8.117) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Num. good news items provided </td>
   <td style="text-align:center;"> −0.170 </td>
   <td style="text-align:center;"> −0.049 </td>
   <td style="text-align:center;"> 2.619 </td>
  </tr>
  <tr>
   <td style="text-align:left;box-shadow: 0px 1px">  </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (0.102) </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (0.091) </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (3.013) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Num.Obs. </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 99 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> R2 </td>
   <td style="text-align:center;"> 0.621 </td>
   <td style="text-align:center;"> 0.495 </td>
   <td style="text-align:center;"> 0.172 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> R2 Adj. </td>
   <td style="text-align:center;"> 0.601 </td>
   <td style="text-align:center;"> 0.479 </td>
   <td style="text-align:center;"> 0.127 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> AIC </td>
   <td style="text-align:center;"> 253.2 </td>
   <td style="text-align:center;"> 259.3 </td>
   <td style="text-align:center;"> 931.9 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> BIC </td>
   <td style="text-align:center;"> 271.4 </td>
   <td style="text-align:center;"> 272.3 </td>
   <td style="text-align:center;"> 950.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> RMSE </td>
   <td style="text-align:center;"> 0.80 </td>
   <td style="text-align:center;"> 0.84 </td>
   <td style="text-align:center;"> 24.95 </td>
  </tr>
</tbody>
</table>

</div>
</div>
</section>
</section>
<section id="treatment-effect-heterogeneity" class="level2">
<h2 class="anchored" data-anchor-id="treatment-effect-heterogeneity">Treatment effect heterogeneity</h2>
<p>We expect that the “good news” treatments would make a bigger difference (for both sets of hypotheses above) among respondents whose pre-treatment beliefs are more pessimistic about climate change (and therefore whose beliefs would potentially be shifted by treatment to a greater extent). We will create a measure of respondents’ pessimism relative to the correct answer on our “good news” items, as follows:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb17"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>dat <span class="sc">|&gt;</span> </span>
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">pessimism_jobs =</span> <span class="sc">-</span><span class="dv">1</span><span class="sc">*</span><span class="fu">as.integer</span>(know_jobs) <span class="sc">+</span> <span class="dv">5</span>,</span>
<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a>         <span class="at">pessimism_co2_change =</span> <span class="sc">-</span><span class="dv">1</span><span class="sc">*</span><span class="fu">as.integer</span>(know_co2_change) <span class="sc">+</span> <span class="dv">5</span>,</span>
<span id="cb17-4"><a href="#cb17-4" aria-hidden="true" tabindex="-1"></a>         <span class="at">pessimism_solar =</span> <span class="fu">as.integer</span>(know_co2_change) <span class="sc">-</span> <span class="dv">1</span>,</span>
<span id="cb17-5"><a href="#cb17-5" aria-hidden="true" tabindex="-1"></a>         <span class="at">pessimism_index =</span> (pessimism_jobs <span class="sc">+</span> pessimism_co2_change <span class="sc">+</span> pessimism_solar)<span class="sc">/</span><span class="dv">12</span>,</span>
<span id="cb17-6"><a href="#cb17-6" aria-hidden="true" tabindex="-1"></a>         <span class="at">pessimism_tercile =</span> <span class="fu">factor</span>(<span class="fu">ntile</span>(pessimism_index, <span class="at">n =</span> <span class="dv">3</span>), <span class="at">levels =</span> <span class="fu">c</span>(<span class="st">"1"</span>, <span class="st">"2"</span>, <span class="st">"3"</span>), <span class="at">ordered =</span> T)) <span class="ot">-&gt;</span> dat2</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Then we will repeat the six tests above, adding an interaction between <code>pessimism_tercile</code> and the number of pieces of good news provided:</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb18"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>concern_reg_het <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(concern_index <span class="sc">~</span> n_good_news_wo_ira<span class="sc">*</span>pessimism_tercile <span class="sc">+</span> <span class="fu">as.integer</span>(concern_cc_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con), <span class="at">data =</span> dat2)</span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>emissions_reg_het <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(<span class="fu">as.integer</span>(emissions_prediction) <span class="sc">~</span> n_good_news_wo_ira<span class="sc">*</span>pessimism_tercile <span class="sc">+</span> <span class="fu">as.integer</span>(concern_cc_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con), <span class="at">data =</span> dat2)</span>
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a>efficacy_reg_het <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(combined_efficacy_post <span class="sc">~</span> n_good_news_wo_ira<span class="sc">*</span>pessimism_tercile <span class="sc">+</span> <span class="fu">as.integer</span>(efficacy_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con), <span class="at">data =</span> dat2)</span>
<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a>wtp_reg_het <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(<span class="fu">as.integer</span>(wtp_taxes) <span class="sc">~</span> n_good_news_wo_ira<span class="sc">*</span>pessimism_tercile <span class="sc">+</span> <span class="fu">as.integer</span>(concern_cc_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con) <span class="sc">+</span> <span class="fu">as.integer</span>(hh_income) <span class="sc">+</span> hh_income_missing, <span class="at">data =</span> dat2)</span>
<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a>ira_reg_het <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(<span class="fu">as.integer</span>(ira_response) <span class="sc">~</span> n_good_news_wo_ira<span class="sc">*</span>pessimism_tercile <span class="sc">+</span> <span class="fu">as.integer</span>(concern_cc_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con), <span class="at">data =</span> dat2)</span>
<span id="cb18-6"><a href="#cb18-6" aria-hidden="true" tabindex="-1"></a>donate_reg_het <span class="ot">&lt;-</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(donate_amount_4 <span class="sc">~</span> n_good_news_wo_ira<span class="sc">*</span>pessimism_tercile <span class="sc">+</span> <span class="fu">as.integer</span>(concern_cc_pre) <span class="sc">+</span> <span class="fu">as.integer</span>(lib_con) <span class="sc">+</span> <span class="fu">as.integer</span>(hh_income) <span class="sc">+</span> hh_income_missing, <span class="at">data =</span> dat2)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb19"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>modelsummary<span class="sc">::</span><span class="fu">modelsummary</span>(<span class="at">models =</span> <span class="fu">list</span>(<span class="st">"Expected emissions"</span> <span class="ot">=</span> emissions_reg_het,</span>
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a>                                         <span class="st">"Concern"</span> <span class="ot">=</span> concern_reg_het,</span>
<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a>                                         <span class="st">"Efficacy"</span> <span class="ot">=</span> efficacy_reg_het,</span>
<span id="cb19-4"><a href="#cb19-4" aria-hidden="true" tabindex="-1"></a>                                         <span class="st">"Willingness to pay higher taxes"</span> <span class="ot">=</span> wtp_reg_het,</span>
<span id="cb19-5"><a href="#cb19-5" aria-hidden="true" tabindex="-1"></a>                                         <span class="st">"Support for aggressive US policy"</span> <span class="ot">=</span> ira_reg_het,</span>
<span id="cb19-6"><a href="#cb19-6" aria-hidden="true" tabindex="-1"></a>                                         <span class="st">"Donation"</span> <span class="ot">=</span> donate_reg_het),</span>
<span id="cb19-7"><a href="#cb19-7" aria-hidden="true" tabindex="-1"></a>                           <span class="at">coef_map =</span> <span class="fu">c</span>(<span class="st">"(Intercept)"</span> <span class="ot">=</span> <span class="st">"Intercept"</span>,</span>
<span id="cb19-8"><a href="#cb19-8" aria-hidden="true" tabindex="-1"></a>                                        <span class="st">"n_good_news_wo_ira"</span> <span class="ot">=</span> <span class="st">"Num. good news items provided"</span>,</span>
<span id="cb19-9"><a href="#cb19-9" aria-hidden="true" tabindex="-1"></a>                                        <span class="st">"pessimism_tercile.L"</span> <span class="ot">=</span> <span class="st">"Medium pessimism"</span>,</span>
<span id="cb19-10"><a href="#cb19-10" aria-hidden="true" tabindex="-1"></a>                                        <span class="st">"pessimism_tercile.Q"</span> <span class="ot">=</span> <span class="st">"High pessimism"</span>,</span>
<span id="cb19-11"><a href="#cb19-11" aria-hidden="true" tabindex="-1"></a>                                        <span class="st">"n_good_news_wo_ira:pessimism_tercile.L"</span> <span class="ot">=</span> <span class="st">"Num. good news X medium pessimism"</span>,</span>
<span id="cb19-12"><a href="#cb19-12" aria-hidden="true" tabindex="-1"></a>                                        <span class="st">"n_good_news_wo_ira:pessimism_tercile.Q"</span> <span class="ot">=</span> <span class="st">"Num. good news X high pessimism"</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">

<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:center;"> Expected emissions </th>
   <th style="text-align:center;"> Concern </th>
   <th style="text-align:center;"> Efficacy </th>
   <th style="text-align:center;"> Willingness to pay higher taxes </th>
   <th style="text-align:center;"> Support for aggressive US policy </th>
   <th style="text-align:center;"> Donation </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Intercept </td>
   <td style="text-align:center;"> 3.332 </td>
   <td style="text-align:center;"> −0.156 </td>
   <td style="text-align:center;"> −0.031 </td>
   <td style="text-align:center;"> −0.060 </td>
   <td style="text-align:center;"> 0.892 </td>
   <td style="text-align:center;"> −8.485 </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:center;"> (0.567) </td>
   <td style="text-align:center;"> (0.039) </td>
   <td style="text-align:center;"> (0.068) </td>
   <td style="text-align:center;"> (0.335) </td>
   <td style="text-align:center;"> (0.345) </td>
   <td style="text-align:center;"> (8.305) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Num. good news items provided </td>
   <td style="text-align:center;"> −0.231 </td>
   <td style="text-align:center;"> −0.002 </td>
   <td style="text-align:center;"> 0.013 </td>
   <td style="text-align:center;"> −0.152 </td>
   <td style="text-align:center;"> −0.057 </td>
   <td style="text-align:center;"> 3.044 </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:center;"> (0.164) </td>
   <td style="text-align:center;"> (0.015) </td>
   <td style="text-align:center;"> (0.011) </td>
   <td style="text-align:center;"> (0.093) </td>
   <td style="text-align:center;"> (0.095) </td>
   <td style="text-align:center;"> (3.028) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Medium pessimism </td>
   <td style="text-align:center;"> 0.436 </td>
   <td style="text-align:center;"> 0.066 </td>
   <td style="text-align:center;"> 0.010 </td>
   <td style="text-align:center;"> −0.091 </td>
   <td style="text-align:center;"> 0.197 </td>
   <td style="text-align:center;"> 3.703 </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:center;"> (0.532) </td>
   <td style="text-align:center;"> (0.049) </td>
   <td style="text-align:center;"> (0.044) </td>
   <td style="text-align:center;"> (0.295) </td>
   <td style="text-align:center;"> (0.310) </td>
   <td style="text-align:center;"> (6.171) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> High pessimism </td>
   <td style="text-align:center;"> 0.534 </td>
   <td style="text-align:center;"> 0.047 </td>
   <td style="text-align:center;"> 0.032 </td>
   <td style="text-align:center;"> 0.369 </td>
   <td style="text-align:center;"> −0.029 </td>
   <td style="text-align:center;"> 7.285 </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:center;"> (0.489) </td>
   <td style="text-align:center;"> (0.042) </td>
   <td style="text-align:center;"> (0.045) </td>
   <td style="text-align:center;"> (0.248) </td>
   <td style="text-align:center;"> (0.298) </td>
   <td style="text-align:center;"> (7.258) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Num. good news X medium pessimism </td>
   <td style="text-align:center;"> −0.078 </td>
   <td style="text-align:center;"> −0.027 </td>
   <td style="text-align:center;"> 0.007 </td>
   <td style="text-align:center;"> −0.034 </td>
   <td style="text-align:center;"> −0.044 </td>
   <td style="text-align:center;"> −4.893 </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:center;"> (0.286) </td>
   <td style="text-align:center;"> (0.028) </td>
   <td style="text-align:center;"> (0.022) </td>
   <td style="text-align:center;"> (0.176) </td>
   <td style="text-align:center;"> (0.174) </td>
   <td style="text-align:center;"> (4.671) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Num. good news X high pessimism </td>
   <td style="text-align:center;"> −0.195 </td>
   <td style="text-align:center;"> −0.017 </td>
   <td style="text-align:center;"> −0.008 </td>
   <td style="text-align:center;"> −0.255 </td>
   <td style="text-align:center;"> 0.109 </td>
   <td style="text-align:center;"> −1.708 </td>
  </tr>
  <tr>
   <td style="text-align:left;box-shadow: 0px 1px">  </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (0.286) </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (0.025) </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (0.021) </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (0.151) </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (0.167) </td>
   <td style="text-align:center;box-shadow: 0px 1px"> (5.175) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Num.Obs. </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 100 </td>
   <td style="text-align:center;"> 99 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> R2 </td>
   <td style="text-align:center;"> 0.068 </td>
   <td style="text-align:center;"> 0.828 </td>
   <td style="text-align:center;"> 0.743 </td>
   <td style="text-align:center;"> 0.634 </td>
   <td style="text-align:center;"> 0.505 </td>
   <td style="text-align:center;"> 0.195 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> R2 Adj. </td>
   <td style="text-align:center;"> −0.002 </td>
   <td style="text-align:center;"> 0.815 </td>
   <td style="text-align:center;"> 0.724 </td>
   <td style="text-align:center;"> 0.598 </td>
   <td style="text-align:center;"> 0.468 </td>
   <td style="text-align:center;"> 0.114 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> AIC </td>
   <td style="text-align:center;"> 378.9 </td>
   <td style="text-align:center;"> −127.5 </td>
   <td style="text-align:center;"> −108.1 </td>
   <td style="text-align:center;"> 257.7 </td>
   <td style="text-align:center;"> 265.2 </td>
   <td style="text-align:center;"> 937.0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> BIC </td>
   <td style="text-align:center;"> 402.4 </td>
   <td style="text-align:center;"> −104.1 </td>
   <td style="text-align:center;"> −84.6 </td>
   <td style="text-align:center;"> 286.3 </td>
   <td style="text-align:center;"> 288.6 </td>
   <td style="text-align:center;"> 965.5 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> RMSE </td>
   <td style="text-align:center;"> 1.47 </td>
   <td style="text-align:center;"> 0.12 </td>
   <td style="text-align:center;"> 0.13 </td>
   <td style="text-align:center;"> 0.79 </td>
   <td style="text-align:center;"> 0.83 </td>
   <td style="text-align:center;"> 24.59 </td>
  </tr>
</tbody>
</table>

</div>
</div>
<p>We will report raw p-values and use the simulation procedure above to identify the highest p-value threshold such that we reject the null hypothesis for the higher pessimism interaction in no more than .05 of simulations within each hypothesis family. The rationale here is that we will make a claim about heterogeneity separately for hypothesis family A and hypothesis family B, and we want to limit the false positive rate for those claims.</p>
</section>
<section id="analysis-of-effects-of-individual-information-treatments" class="level2">
<h2 class="anchored" data-anchor-id="analysis-of-effects-of-individual-information-treatments">Analysis of effects of individual information treatments</h2>
<p>We will also report the results of providing each information treatment separately. This includes the three pieces of good news above plus two others.</p>
<p>First we will also look at an information treatment we provided that stated that the US gas tax is the lowest in the OECD and mentioned that over 20 OECD countries have a tax that is at last 10 times as high. This information treatment could arguably be lumped with the other pieces of “good news” above because it emphasizes that others are taking strong action, but it also highlights the limited US response so far, which could tend to work in the opposite direction to the other information treatments. We therefore exclude it from the “number of pieces of good news” analysis above, and instead analyze it separately here.</p>
<p>Second we will also look at the effect of informing respondents about the IRA before vs after asking for the respondent’s other attitudes. This comes from our randomization of question order: we ask the donation question last to everyone, but for half the respondents we ask about (and inform about) the IRA before asking about willingness to pay taxes, concern about climate change, expectations about global emissions, while for the other half we ask about the IRA after asking these other questions. Thus question order determines whether the respondent is made aware of the IRA before being asked for other policy preferences (but not the IRA question or the donation outcome).</p>
<p>For each of these five information treatments, and for each of the two families of three outcomes above, we will measure the effect of the binary provision of information. This is fifteen tests per family. We will report raw p-values and report which nulls can be rejected in each family after applying simulation-based MHT corrections as described above.</p>
<div class="cell">
<div class="sourceCode cell-code" id="cb20"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>treatments <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">"solar_cost_info"</span>, <span class="st">"jobs_info"</span>, <span class="st">"us_emissions_info"</span>, <span class="st">"gas_tax_info"</span>, <span class="st">"FL_39_DO"</span>)</span>
<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a>outcomes <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">"as.integer(emissions_prediction)"</span>, <span class="st">"concern_index"</span>, <span class="st">"combined_efficacy_post"</span>, <span class="st">"as.integer(wtp_taxes)"</span>, <span class="st">"as.integer(ira_response)"</span>, <span class="st">"donate_amount_4"</span>)</span>
<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a>outcome_labels <span class="ot">=</span> <span class="fu">c</span>(<span class="st">"Expected emissions"</span>, <span class="st">"Concern"</span>, <span class="st">"Efficacy"</span>, <span class="st">"Willingness to pay higher taxes"</span>, <span class="st">"Support for aggressive US policy"</span>, <span class="st">"Donation"</span>)</span>
<span id="cb20-4"><a href="#cb20-4" aria-hidden="true" tabindex="-1"></a>controls <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">"as.integer(concern_cc_pre) + as.integer(lib_con)"</span>, <span class="st">"as.integer(concern_cc_pre) + as.integer(lib_con)"</span>, <span class="st">"as.integer(efficacy_pre) + as.integer(lib_con)"</span>, <span class="st">"as.integer(concern_cc_pre) + as.integer(lib_con) + as.integer(hh_income) + hh_income_missing"</span>, <span class="st">"as.integer(efficacy_pre) + as.integer(lib_con)"</span>,<span class="st">"as.integer(concern_cc_pre) + as.integer(lib_con) + as.integer(hh_income) + hh_income_missing"</span>)</span>
<span id="cb20-5"><a href="#cb20-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb20-6"><a href="#cb20-6" aria-hidden="true" tabindex="-1"></a><span class="fu">expand_grid</span>(<span class="fu">tibble</span>(<span class="at">treatment =</span> treatments),</span>
<span id="cb20-7"><a href="#cb20-7" aria-hidden="true" tabindex="-1"></a>            <span class="fu">tibble</span>(<span class="at">outcome =</span> outcomes,</span>
<span id="cb20-8"><a href="#cb20-8" aria-hidden="true" tabindex="-1"></a>                   <span class="at">outcome_label =</span> outcome_labels,</span>
<span id="cb20-9"><a href="#cb20-9" aria-hidden="true" tabindex="-1"></a>                   <span class="at">controls =</span> controls)) <span class="sc">|&gt;</span> </span>
<span id="cb20-10"><a href="#cb20-10" aria-hidden="true" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">the_formula =</span> <span class="fu">map</span>(<span class="fu">str_c</span>(outcome, <span class="st">" ~ "</span>, treatment, <span class="st">" + "</span>, controls), as.formula),</span>
<span id="cb20-11"><a href="#cb20-11" aria-hidden="true" tabindex="-1"></a>         <span class="at">reg =</span> <span class="fu">map</span>(the_formula, <span class="sc">~</span> estimatr<span class="sc">::</span><span class="fu">lm_robust</span>(<span class="at">formula =</span> .x, <span class="at">data =</span> dat2))) <span class="ot">-&gt;</span> info_treatment_regs  </span>
<span id="cb20-12"><a href="#cb20-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb20-13"><a href="#cb20-13" aria-hidden="true" tabindex="-1"></a><span class="co"># we will report the results based on this information:</span></span>
<span id="cb20-14"><a href="#cb20-14" aria-hidden="true" tabindex="-1"></a>info_treatment_regs <span class="sc">|&gt;</span> </span>
<span id="cb20-15"><a href="#cb20-15" aria-hidden="true" tabindex="-1"></a>  <span class="fu">select</span>(treatment, outcome_label, reg) <span class="sc">|&gt;</span> </span>
<span id="cb20-16"><a href="#cb20-16" aria-hidden="true" tabindex="-1"></a>  <span class="fu">mutate</span>(<span class="at">tidied =</span> <span class="fu">map</span>(reg, broom<span class="sc">::</span>tidy)) <span class="sc">|&gt;</span> </span>
<span id="cb20-17"><a href="#cb20-17" aria-hidden="true" tabindex="-1"></a>  <span class="fu">select</span>(<span class="sc">-</span>reg) <span class="sc">|&gt;</span> </span>
<span id="cb20-18"><a href="#cb20-18" aria-hidden="true" tabindex="-1"></a>  <span class="fu">unnest</span>(tidied) <span class="sc">|&gt;</span> </span>
<span id="cb20-19"><a href="#cb20-19" aria-hidden="true" tabindex="-1"></a>  <span class="fu">filter</span>(<span class="fu">str_detect</span>(term, <span class="st">"included"</span>) <span class="sc">|</span> (<span class="fu">str_detect</span>(term, <span class="st">"FL_39"</span>) <span class="sc">&amp;</span> <span class="sc">!</span>outcome_label <span class="sc">%in%</span> <span class="fu">c</span>(<span class="st">"Support for aggressive US policy"</span>, <span class="st">"Donation"</span>)))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-stdout">
<pre><code># A tibble: 28 × 11
   treatm…¹ outco…² term  estimate std.e…³ stati…⁴ p.value conf.…⁵ conf.…⁶    df
   &lt;chr&gt;    &lt;chr&gt;   &lt;chr&gt;    &lt;dbl&gt;   &lt;dbl&gt;   &lt;dbl&gt;   &lt;dbl&gt;   &lt;dbl&gt;   &lt;dbl&gt; &lt;dbl&gt;
 1 solar_c… Expect… sola… -0.378    0.299  -1.27    0.209  -0.972   0.215     96
 2 solar_c… Concern sola…  0.00193  0.0249  0.0774  0.938  -0.0475  0.0513    96
 3 solar_c… Effica… sola…  0.0255   0.0252  1.01    0.313  -0.0244  0.0755    96
 4 solar_c… Willin… sola… -0.358    0.172  -2.08    0.0406 -0.700  -0.0157    94
 5 solar_c… Suppor… sola… -0.138    0.184  -0.751   0.455  -0.503   0.227     96
 6 solar_c… Donati… sola…  4.84     6.00    0.806   0.422  -7.08   16.8       93
 7 jobs_in… Expect… jobs… -0.180    0.308  -0.584   0.560  -0.791   0.431     96
 8 jobs_in… Concern jobs… -0.00625  0.0248 -0.253   0.801  -0.0554  0.0429    96
 9 jobs_in… Effica… jobs…  0.0366   0.0266  1.38    0.171  -0.0161  0.0894    96
10 jobs_in… Willin… jobs… -0.166    0.174  -0.954   0.342  -0.511   0.179     94
# … with 18 more rows, 1 more variable: outcome &lt;chr&gt;, and abbreviated variable
#   names ¹​treatment, ²​outcome_label, ³​std.error, ⁴​statistic, ⁵​conf.low,
#   ⁶​conf.high</code></pre>
</div>
</div>
<p>We will also test whether the effect of the four information treatments (not the IRA question order treatment, because we don’t have a pessimism measure there) is larger for respondents who were more pessimistic on the relevant knowledge question, as above, and address MHT to limit false positives about treatment effect heterogeneity claims within hypothesis families as above.</p>
</section>
<section id="exploratory-analysis" class="level2">
<h2 class="anchored" data-anchor-id="exploratory-analysis">Exploratory analysis</h2>
<p>In addition to the hypothesis tests above, we will report some exploratory analysis investigating correlates of knowledge and pessimism.</p>
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